We investigate the behavior of a Josephson junction consisting of a ferromagnetic insulator-superconductor (FI-S) bilayer tunnel-coupled to a superconducting electrode. We show that the Josephson coupling in the structure is strenghtened by the presence of the spin-splitting field induced in the FI-S bilayer. Such strenghtening manifests itself as an increase of the critical current $I_c$ with the amplitude of the exchange field. Furthermore, the effect can be strongly enhanced if the junction is taken out of equilibrium by a temperature bias. We propose a realistic setup to assess experimentally the magnitude of the induced exchange field, and predict a drastic deviation of the $I_c(T)$ curve ($T$ is the temperature) with respect to equilibrium.
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